Computation rule



Aug. 9, 19327. M. o. scHUR COMPUTATION RULE Filed May 12, 1927 7 N rk v vw m. N. www E: .Q T L. Q

Patented Aug. 9, 1932 UNITED sTATEs. PATENT OFFICE MILTON 0. SCHUR, 0F BERLIN, NEW HAMPSHIRE, ASSIGNOR '10 BROWN COMPANY, 0E BERLIN, NEW HAMPSHIRE, A CORPORATION OF MAINE.

COMPU'IATION RULE Application led May 12, 1927. Serial No. 190,772. p

This invention relates to computation rules, and has for its object to provide a rule which is simple in construction and which may be easily, rapidly, and accurately operated by Untrained men.

In mill practice, it is sometimes necessary to solve equations of a certain general type a great many times, so that it becomes highly desirable to use a computation rule for such purpose. The average untrained mill operator, however, nds difficulty in using the usual slide rule for this purpose, particularly when certain of the factors in the equation are complexterms. Thus, it may be necessary to solve an equationinvolving three variables of the general type:

where is the unknown factor to be solved for, and where y and .e are known factors which may be complex terms.

Similarly, it may be necessary to solve an equation involving four variables of the genor origin. v

Where an equation of the general type:

is to be solved, the rule comprises a single, uniformly extensible, or stretchable linear scale lixedat one end andv preferably correspondin to the unknown factor Adjacent an parallel to this scale are two fixed linear or substantially linear scales,one corresponding to the known factor y and the other to the known factor z, and both having their origins in line with the origin of the extensible scale.

It is manifest that when 2 equals unity and the same modulus is used for both the scales y and the scale y, if superposed' on the scale will coincide therewith. But when z equals 2, the sca-le of must be extended to double its length if under any value 0f g/ is still to be found the corresponding value of Similarly, nif a equals 21/2, 3, or any number n, the scale of must be extended to 21/2, 3 or n times its initial length (i. e., the length when 2 equals l), in order that the corresponding value of may be found under any value of y. The insertion ofa constant factor in the equation to change it to :v

merely requires that the modulus of one or more o f the scales be changed according to convenience.

Where an equation of the general type n 52:2 wKz is being solved, the rule com rises two uniformly extensible linear sca es, each fixed at one end, one corresponding to the unknown factor and the other to the known factor y; Adjacent and parallel to thescale m, is a fixed linear or substantially linear scale corresponding to the known factor z, and adjacent and parallel to the scale y is a fixed linear or su stantially linear scale coresponding to the factor w. When the scale a: is extended until a properly chosen mark upon it is opposite to the known factor on the scale a, and the scale y extended until a predetermined mark upon it is opposite the known factor on the scale w, the distance from the origin to the unknown factor on scale m is proportional t to times e. Similarly, the dlstance from the origin to the known factor on scale y is proportional to w times y. rIhe moduli of the scales having been correctly chosen, di-

rectly oppositethe known factor on the scale y will be found the unknown factor w.

objects in view, the invention preferably consists of the following construction, arrangement, and combination of parts, which will hereinafter be described in conjunction with the accompanying drawing, wherein v Figure 1 illustrates a rule with a single extensible scale. j Figure 2 represents the lower end portion of the rule enlarged.

Figure 3 illustrates a rule with multiple are linear and thescale i-s very nearly linear, Y

extensible scales.-

Figure 4 represents the lower end portion of the rule enlarged. Referring to Figure 1 of the drawing1 indicates a base to one end of which an extensible scale 2 of-substantially uniform elasticity is fixed, as b a clamp 3. The scale as shown, is preferab y composed of elastic rubber, but, if desired, a uniform coil spring,

lazy tongs, or other uniformly extensible means may be employed. Adjacent and parallel to the scale 2 are the fixed scales 4 and 5, which, as shown, are laid off on the base. The origin or zero point of all the scales lies on a line coinciding with the inner edge O of the clamp, that is, where the extensible scale 2 just begins to stretch.

This rule may be employed to solve an equation involving three variables, and nds utility, for example, in a pulp mill where a treatment of pulp with caustic soda solution is being performed to effect a solution of certain components from the pulp. To control such a treatment, it is necessary to determine the alkalinity of the pulp while being treated.

For this purpose,the stock density or per cent. weight of dry fiber in the pulp islascertained, and a definite volume of solution expressed from'the pulp being treated is titrated with standardized acid. The alkalinity is then calculated, by the following equation scale 4 likewise corresponds to the known linear variable C; and the fixed scale 5 corresponds tol-I-y which varies very nearly lineally throughout the range of stock densities employed in the treatment.

The operation of the rule is as follows. The end of the scale 2 is pulled or stretched until a certain point, such as an arrow 6. thereon,

s per cent. weight of dry ber in the v points to 4the graduation representing the stock density yfound, in.the""pulp. 0n the stretched scale 2, Whose graduations represent the value N, will'now be found the `per cent. caustic soda in the pulp, based on stock, di-

rectly opposite the graduationon the fixed scale 4 representing thenuniber of cubic centimeters vof ,standardized acid 'used in .titratinglzthe sample solutionexpressed from the vpup-f 1 Y ...Itisobvious that, since the scales 2 4and 4 a stretch rule sucli'fasfdesjcribed is very'easyv i' throughwthe inclusi-on of theJ tfn s a j s i single factory in .scale 5 anadditional important simplification is'gained, for when a slide rule is used to compute N ,f not only doy the logarithmic scales confuse :the average mill operator, but the mentalv arithmetic in- D 1 b6- fore the iinal product is obtained, frequently leads to error. While itis-,possible to arvolved in arriving at a value for range a table with values of D at, say, the,

heads of columns, and values to C at the left ends of horizontal rows, nevertheless, in order to cover fully the ranges desired, it

would be necessary to tabulate so many figures that, even though the operator were furnished with a guiding device of some sort, he would be apt to make mistakes.

Where four variables are involved in a calculation, a slide rule or table would be apt to lead to still greater confusion. A case of this sort arises in computing the gallons per minute of bleach liquor necessary to dose unbleached stock in a continuous process, where one mustknow the-rate at which the stock is flowing through the system, the strength of the bleach liquor, and the per cent. bleach desired, based on stock.

` P equalsstock How in terms of tons per 24 hours,

L equals per cent. bleach desired, G equals strength of bleach liquor in grams available chlorine per liter,

B equals gallons per-minute of bleach liquor needed, and K is a constant.

A rule for solving for Bin the foregoing equation is shown in Figure 4, where on a base 10 are clamped at 11 two uniformly extensible scales 12 and 13, the scale 12 corresponding to the factor L, and the scale 13 to the factor B. On the base adjacent to the scale 12 is laid offa scale 14, corresponding to P, and adjacent to the scale 13 a scale15 corresponding to G. Preferably, therule is provided with means for holding eitheror both of the extensible scales in position after stretching. As shown, this is accomplished by fixing a peg to the upper end of, say, the scale 12 and forming a series of openings in the base adjacent to the graduations on the scale 14, so that after stretching the scale, the peg may be inserted into the proper opening to hold the stretched scale in position. This rule is operated as follows. The operator stretches the scale l2 and sticks the peg 17 into one of the holes 16 so as to bring an arrow 18 on the scale 12 directly opposite the graduation on scale 14 corresponding to the rate of stock fiow. He then stretches scale 13 until an arrow 19 thereon lies directly opposite the graduations on scale 15 corresponding to the strength of the bleach liquor at his disposal. He now finds on scale y13 directly opposite the per cent bleach desired on scale 12, the gallons of bleach liquor per minute necessary.

It is apparent that when the arrow 18 is brought opposite the graduation of P under consideration, and the arrow 19 opposite the predetermined scale graduation of G, then the distance from the origin to the desired value of L on scale 12 is proportional to PL.

Similarly, the distance from the origin to the proper value of B on scale 13 is proportional to BG. The moduli of the scales having been correctly chosen, these distances are equal.

Having thus described certain embodiments of this invention, it should be obvious that various changes and modifications might be made Without departing from the spirit 0r scope of invention as defined by the appended claims.

What I claim is:

1. A computation rule comprising a plurality of extensible scales in cooperative relation with one another, said scales each being fixed at one end and being freely extensible from said fixed end.

2. A computation rule comprisng a plurality of adjacent and parallel, uniformly extensible scales, fixed scales adjacent and parallel to said extensible scales, all said scales being in cooperative relation with one another and corresponding to substantially lineally varying factors and having a common line of origin, said extensible scales each being fixed at one end at said ori 'n and being freely extensible from said fixe end.

3. A computation rule comprising a pair of adjacent and parallel extensible scales, each fixed at one end; a fixed scale adjacent and parallel to each of said extensible scales and to certain of whose graduations a point on the corresponding extensible scale may be brought by extending said corresponding extensible scale; said rule including means for holding one of said extensible scales in position after it has been extended.

4. A computation rule comprising'a plurality of extensible scales and a plurality of fixed scales with which said extensible scales are in cooperative relation, said extensible scales each being fixed at one end and being freely extensible from said fixed end.

5. A computation rule comprising a base, a

pair of adjacent scales of extensible material each fixed at one end to said base, a fixed scale on said base adjacent to each of said extensible scales and to certain graduations of which a point on the adjacent extensible scale may be brought by stretching said extensible scale, said rule including means for holding one of said extensible scales in position after stretching.

6. A computation rule comprising a base, a pair of adjacent scales of extensible material each fixed at one en'd to said base, a peg fixed to one of said scales at its free end, and a lixedscale on said base adjacent to each of said extensible scales and to certain graduations of which a point on the adjacent extensible scale may be brought by stretching said extensible scale, said base having a series of openings adjacent to the graduations of one of the fixed scales but beyond the free end of the corresponding extensible scale and into any of which said peg may be inserted to hold its rubber scale in position after stretching.

7. A computation rule comprising a base, a pair of adjacent scales of extensible material and having a uniform cross-section each fixed at one end to said base, and a fixed scale on said base adjacent to each of said extensible scales and to certain graduations of which a point'on the adjacent extensible scale may be brought by stretching said extensible scale, all said scales corresponding to substantially lineally varying factors and having a common line of origin.

In testimony whereof, I have affixed my signature.

MILTON O. SCI-IUR. 

